Radioactive decay flashcards

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Background radiation
Ionising radiation present all the time from natural and artificial sources (radon, rocks, cosmic rays, food and the body, medical uses), with no deliberate source nearby.
Activity A
The number of nuclei in a sample that decay per unit time. Unit: becquerel, 1 Bq = 1 decay per second.
Decay constant λ
The probability per unit time that an individual nucleus will decay (unit s⁻¹, or h⁻¹, year⁻¹ …).
Half-life t½
The average time taken for the number of undecayed nuclei of an isotope (and so its activity) to halve.
Random (radioactive decay)
It is impossible to predict which nucleus will decay next or when a given nucleus will decay; each has the same constant probability of decaying per unit time.
Spontaneous (radioactive decay)
Decay is not caused or affected by external factors such as temperature, pressure or chemical state.
Alpha particle
A helium nucleus, ⁴₂α: 2 protons + 2 neutrons, charge +2e.
Beta-minus and beta-plus particles
β⁻: a fast electron created in the nucleus (charge −e). β⁺: a positron, the antiparticle of the electron (charge +e).
Activity and number of nuclei
A = λN (λ in s⁻¹ for A in Bq) (Yes)
Rate of decay
dN/dt = −λN (Yes)
Decay constant and half-life
λ = ln 2 / t½ (Yes)
Exponential decay of N and of A
N = N₀e^(−λt) and A = A₀e^(−λt) (Yes)
Log forms of the decay equations
ln N = ln N₀ − λt and ln A = ln A₀ − λt (No — derive it: take natural logs)
Fraction left after n half-lives
(½)ⁿ (No — learn it)
Correcting a count rate
corrected count rate = measured count rate − background count rate (No — learn it)
Graph of N (or A) against t
Exponential decay curve: halves every half-life, wherever you start; its gradient at any point is dN/dt = −λN.
Graph of ln A against t
Straight line: gradient = −λ, intercept = ln A₀.
Corrected count rate against lead thickness (Core Practical 15)
Exponential fall; ln C against thickness is a straight line with a negative gradient.
α, β⁻ and β⁺ decay on a chart of Z against N
α: two squares diagonally down-left (Z − 2, N − 2). β⁻: one up-left (Z + 1, N − 1). β⁺: one down-right (Z − 1, N + 1). γ: no move.
Counts in equal time intervals from a long-lived source
Scatter randomly about a mean value — evidence that decay is random.
Why is alpha strongly ionising but short-ranged?
Large charge and slow speed: it ionises many atoms per mm, losing its energy within a few cm of air.
Why is an alpha source most dangerous inside the body?
Inside, the α particles reach living cells directly and deposit all their energy in a small volume of tissue; outside, skin stops them.
Why does a medical tracer emit gamma and have a half-life of hours?
γ escapes the body to the detector and is weakly ionising; a half-life of hours lasts for the scan but leaves little activity afterwards.
How does carbon dating work?
Living things keep a steady C-14 activity per gram of carbon; after death it decays with t½ = 5730 years. Comparing activities gives the age.
Why is count rate smaller than activity?
The detector catches only some of the emissions (others go in other directions or pass through), though the two are proportional for a fixed arrangement.
Why include the neutrino or antineutrino in beta decay?
It is needed to conserve energy, momentum and lepton number; it explains why beta particles have a range of energies.
1350 counts in 5.0 min; background 36 min⁻¹. Corrected count rate?
4.5 s⁻¹ − 0.60 s⁻¹ = 3.9 s⁻¹.
Tc-99m: t½ = 6.0 h, A = 400 MBq. Decay constant and number of nuclei?
λ = 0.693 ÷ 21 600 s = 3.21 × 10⁻⁵ s⁻¹; N = A/λ = 4.00 × 10⁸ ÷ 3.21 × 10⁻⁵ = 1.25 × 10¹³.
80 mg of an isotope with t½ = 15 h. Mass left after 60 h?
60 h = 4 half-lives: 80 × (½)⁴ = 5.0 mg.
Living carbon 0.25 Bq g⁻¹; ancient sample 0.084 Bq g⁻¹; t½ = 5730 y. Age?
t = ln(0.25/0.084) ÷ (0.693/5730) = 9.0 × 10³ years.
ln A falls from 9.20 to 6.43 in 12.0 h. Half-life?
λ = 2.77 ÷ 12.0 = 0.231 h⁻¹; t½ = 0.693 ÷ 0.231 = 3.0 h.
Th-232 (Z = 90) decays to Pb-208 (Z = 82). Number of α and β⁻ decays?
ΔA = 24 → 6 α (Z would drop to 78); 82 − 78 = 4 β⁻.
Before halving, plotting or taking ln of a count rate…
Subtract the background count rate (in the same unit) from every reading.
Units of λ in A = λN
s⁻¹ — convert a half-life in hours, days or years to seconds so that A comes out in Bq.
Checking a nuclear equation
Top numbers (nucleons) and bottom numbers (charge) must each add up to the same total on both sides.
Gradient of ln A against t
Equals −λ: quote it with its sign, then λ = −gradient and t½ = ln 2/λ.
Control variables in the gamma absorption practical
Same source, fixed source–detector distance, same counting time and detector; only the lead thickness changes.

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